两个正数a,b满足4ab+a+b=12,求
问题描述：
两个正数a,b满足4ab+a+b=12,求
(1)ab的取值范围
(2)a+b的取值范围
答
a+b =12-4ab ≥ 2√ab
4ab+2√ab-12 ≤ 0
-1/2 ≤√ab ≤ 2/3
ab≥ 0
0≤ ab ≤4/9
4ab =12 -(a+b) ≤ (a+b)^2
(a+b)^2 +(a+b) -12 ≥ 0
a+b ≥ 3 或a+b ≤-4
正数a,b,a+b ≥ 3